In this study, the \(H_\infty \) control problem of a linear time-delay system is considered. A proportional–integral observer and equivalent-input-disturbance method (the PIO-based-EID method) provides a more accurate estimation of the system state and allows for a more flexible system design for enhanced stability. Therefore, in this study, the method is used to improve the disturbance suppression performance of the system. Firstly, an EID estimate is obtained based on the PIO-based-EID method. Subsequently, a static output-feedback control law including EID estimation is developed to ensure excellent control effect. Thirdly, the stability of the closed-loop system is demonstrated by the results of linear-matrix-inequalities to match the \(H_\infty \) control performance specification. The control law gain and observer gain are then determined using the singular value decomposition method. Ultimately, simulation results from MATLAB software are analyzed to confirm the method’s feasibility.
